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Find common factors

Common factors are positive whole numbers that divide each of two or more whole numbers with no remainder; finding them means generating each number’s factor pairs or divisors and identifying the intersection of the resulting sets. This understanding distinguishes factors from multiples and supports determining the greatest common factor, simplifying fractions, and reasoning about equal groups. The focus is on positive whole numbers and numerical factor relationships, not factors of algebraic expressions or generalized integer factorization.

Detailed Explanation: Find common factors

A common factor is a positive whole number that divides two or more numbers with no remainder.

To find common factors:

  1. List the factor pairs for each number.
  2. Write all the factors in each number’s set.
  3. Identify the numbers that appear in both sets.

Example: Find the common factors of (18)(18) and (24)(24).

First, find the factor pairs of (18)(18):

1×18,2×9,3×61 \times 18,\quad 2 \times 9,\quad 3 \times 6

So the factors of (18)(18) are:

{1,2,3,6,9,18}\{1,2,3,6,9,18\}

Next, find the factor pairs of (24)(24):

1×24,2×12,3×8,4×61 \times 24,\quad 2 \times 12,\quad 3 \times 8,\quad 4 \times 6

So the factors of (24)(24) are:

{1,2,3,4,6,8,12,24}\{1,2,3,4,6,8,12,24\}

Now identify the numbers that appear in both sets:

{1,2,3,6}\{1,2,3,6\}

Therefore, the common factors of (18)(18) and (24)(24) are:

1,2,3, and 6\boxed{1,2,3,\text{ and }6}

Check: each of these numbers divides both (18)(18) and (24)(24) evenly.

Learn by doing: Find common factors

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    Finding Greatest Common Factor

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